The only avi to mve conversion we know about is used by modders of old Interplay games (Infinity engine) that use standard AVI videos to create a video in MVE format that can be used to add or replace existing in-game video.
Once upon a time a tool called PS gui existed, which was a dedicated converter for Infinity engine content and this one could be used for this type of export. Perhaps you can still find it somewhere on the Internet for download, many Infinity game mod tools can be found here.